Proper time derivatives in quantum mechanics

TL;DR

This paper develops various quantum proper time derivatives within relativistic quantum mechanics, linking them to Hamiltonians that act as mass operators, and proposes an extended indefinite mass framework based on Feynman parametrization of the Dirac equation.

Contribution

It introduces new quantum proper time derivatives derived from Beck's approach and formulates an extended indefinite mass framework using Feynman parametrization.

Findings

Derived multiple quantum proper time derivatives from Beck's framework.

Linked Hamiltonians to mass operators in an extended indefinite mass framework.

Connected different parametrizations of the Dirac equation through this framework.

Abstract

Several quantum proper time derivatives are obtained from the Beck one in the usual framework of relativistic quantum mechanics (spin 1/2 case). The ``scalar Hamiltonians'' of these derivatives should be thought of as the conjugate variables of the proper time. Then, the Hamiltonians would play the role of mass operators, suggesting the formulation of an adequate extended indefinite mass framework. We propose and briefly develop the framework corresponding to the Feynman parametrization of the Dirac equation. In such a case we derive the other parametrizations known in the literature, linking the extension of the different proposals of quantum proper time derivatives again.